Even just an ability to add a 5 character prefix to the item name would be handy. It could be seperate from the item name and sortable through it without affecting any scripts.

I fully agree.

A reasonable solution would be to nickname items. For the viewer, it would show the nickname, for the server/script it would show the original name. Maybe even make it like display names (optionally) like

My Favorite Shirt [storename shirt color] (no modify)

This is my response to the people who said we shouldn't be able to rename no mod items because it might break scripts. If that will happen with your creation, just include a notecard with a warning with it. If I'm willing to take the chance on breaking my own object by renaming it, why should I be prevented from doing that?

I usually just make a folder with the name I want for it and drop the item in there. It's not a perfect solution, but it works

An item that lacks the modify permission should not be able to have any of its properties modified except by scripts already installed within that item, without exception, thus allowing operation as intended by the creator of the item and ensuring product stability for end-users. This needs to be the case for creators to be able to trust that the permission system, a fundamental part of creation within Second Life, will not eventually become less useful and meaningful going forward due to requests like this one.

Unfortunately allowing changes to the name property of the item would potentially, and is very likely to, disrupt link-aware script operations using the name property to identify individual links within an object.

While it might be possible for Linden Lab to implement a way to rename inventory links/aliases without altering the original object that would probably significantly complicate their creation, use, and implementation. That being said I wouldn't be opposed to such an option, and such may need to be looked into further and carefully weighed by Linden Lab, though it likely should get its own feedback request.

The best solution at this time would be to create a folder in your inventory with the desired name and place the item, or a copy of the item, into that folder. This may not be your ideal solution but folders are just as searchable as objects are in your inventory and this solution causes essentially no added overhead for Linden Lab nor does it require any alterations to the server or viewer.

This solution might work for everyone.

The ability to make a shortcut to an inventory item and for the shortcut to be re-nameable without effecting the original object. This way you can put the original objects in a sub-folder somewhere and work exclusively with shortcuts that you can rename as you see fit.

As others have said creators (myself included) have relied on the no-mod nature of an object to maintain the name, description and inventory contents. Any ability to alter that can have undesirable effects and in some cases even bypass more advanced permission systems implemented by creators.

One of the major perks of no-mod is scripting complicated items where the name or description are used to identify parts of a link set. As others have mentioned, the ability to rely on the no mod property likely has other uses that have depended upon it, including checking things like the name and Creator as a reliable way to identify an item.

But I like the idea about organizing the inventory and I want the feature, so what about if there was the ability to rename the no mod asset when it's inside the inventory, and to use the actual name of the item when it's rezzed in the world?

Making no mod items able to be renamed make's it harder for us to script ban unwated items from entering are regions.

I've hoped for this for 15 years, but I understand that NO MOD probably really means NO MOD. My answer has been to put something in a folder and change THAT name to the one I want. Not great, but certainly helps.